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<title>Problem 2102. -- [Usaco2010 Dec]The Trough Game -- 衡阳八中OJ离线版-2012-02-29</title><center><h2>2102: [Usaco2010 Dec]The Trough Game</h2><span class=green>Time Limit: </span>10 Sec&nbsp;&nbsp;<span class=green>Memory Limit: </span>64 MB<br><span class=green>Submit: </span>50&nbsp;&nbsp;<span class=green>Solved: </span>35<br>[<a href='submitpage.php?id=2102'>Submit</a>][<a href='problemstatus.php?id=2102'>Status</a>][<a href='bbs.php?id=2102'>Discuss</a>]</center><h2>Description</h2><div class=content>Farmer John and Bessie are playing games again. This one has to do
with troughs of water.

Farmer John has hidden N (1 <= N <= 20) troughs behind the barn,
and has filled some of them with food. Bessie has asked M (1 <= M
<= 100) questions of the form, "How many troughs from this list
(which she recites) are filled?".

Bessie needs your help to deduce which troughs are actually filled.

Consider an example with four troughs where Bessie has asked these
questions (and received the indicated answers):

    1) "How many of these troughs are filled: trough 1"
       -->  1 trough is filled

    2) "How many of these troughs are filled: troughs 2 and 3"
       -->  1 trough is filled

    3) "How many of these troughs are filled: troughs 1 and 4"
       -->  1 trough is filled

    4) "How many of these troughs are filled: troughs 3 and 4"
       -->  1 trough is filled

From question 1, we know trough 1 is filled.
From question 3, we then know trough 4 is empty.
From question 4, we then know that trough 3 is filled.
From question 2, we then know that trough 2 is empty.

求N位二进制数X，使得给定的M个数，满足X and Bi=Ci ,Bi ci分别是读入的两个数
</div><h2>Input</h2><div class=content>* Line 1: Two space-separated integers: N and M

* Lines 2..M+1: A subset of troughs, specified as a sequence of
        contiguous N 0's and 1's, followed by a single integer that is
        the number of troughs in the specified subset that are filled.

</div><h2>Output</h2><div class=content>* Line 1: A single line with:

  * The string "IMPOSSIBLE" if there is no possible set of filled troughs 
    compatible with Farmer John's answers.

  * The string "NOT UNIQUE" if Bessie cannot determine from the given data 
    exactly what troughs are filled.

  * Otherwise, a sequence of contiguous N 0's and 1's specifying
    which troughs are filled.


</div><h2>Sample Input</h2>
			<div class=content><span class=sampledata>4 4<br />
1000 1<br />
0110 1<br />
1001 1<br />
0011 1<br />
</span></div><h2>Sample Output</h2>
			<div class=content><span class=sampledata>1010<br />
</span></div><h2>HINT</h2>
			<div class=content><p></p></div><h2>Source</h2>
			<div class=content><p><a href='problemset.html?search=Silver'>Silver</a></p></div><center>[<a href='submitpage.php?id=2102'>Submit</a>][<a href='problemstatus.php?id=2102'>Status</a>][<a href='bbs.php?id=2102'>Discuss</a>]</center>﻿<br>

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